WORKSHOP ON ENGINEERING MATHEMATICS AND COMPUTATIONAL ELECTROMAGNETICS

Transcription

1 WORKSHOP ON ENGINEERING MATHEMATICS AND COMPUTATIONAL ELECTROMAGNETICS TIME: WEDNESDAY, MAY 13 TH, 2015 LOCATION: U2-046, VÄSTERÅS, MDH ORGANIZERS: PROF. SERGEI SILVESTROV AND DR. MILICA RANČIĆ RESEARCH ENVIRONMENT MATHEMATICS AND APPLIED MATHEMATICS (MAM) DIVISION O F APPLIED MATHEMATIC S SCHOOL OF EDUCATION, CULTURE AND COMMUNICATION (UKK) Workshop s overall mission and scope This international interdisciplinary workshop on Engineering Mathematics and Computational Electromagnetics is focused on interdisciplinary co-production and collaboration with other universities nationally and internationally, industry, research laboratories and institutes, municipality and the surrounding community as one of the main priorities of the Mathematics and Applied Mathematics (MAM) research environment at the School of Education, Culture and Communication (UKK) at Mälardalen University. Applications of Mathematics in different fields of electromagnetics will be illustrated through lectures by researchers from both academia and industry from Sweden, Serbia, Estonia, and France. The speakers will cover a wide range of interesting subjects from engineering mathematics applications in natural and life sciences, health and electromagnetics technologies such as: lightning, grounding, antenna analysis, bioelectromagnetics, and related areas. We hope you will find this workshop both informative and educational. Welcome!

2 TIME SCHEDULE: 10:00 OPENING - SERGEI SILVESTROV (SWEDEN) LECTURE 1 Victor Abramov (ESTONIA) 10:00 10:45 10:50 11:35 11:40 12:25 University of Tartu, Institute of Mathematics Title: Maxwell Equations, Differential Forms, Yang-Mills Theory and Connections LECTURE 2 Jean-Pierre Bérenger (FRANCE) LEAT Université Nice Sophia Antipolis CNRS Title: The Evanescent Solutions of the Maxwell Equations LECTURE 3 Nenad Cvetković (SERBIA) University of Niš, ELFAK, Department of Theoretical Electrical Engineering Title: Application of the Green s Function to the Quasi-Stationary Analysis of Grounding Systems in Non-Homogeneous Soil 12:30 14:00 LUNCH BREAK LECTURE 4 Magnus Otterskog (SWEDEN) 14:00 14:45 14:50 15:15 Mälardalen University, School of Innovation, Design and Engineering Title: Reducing the Computational Time of Inverse Scattering Problems Thorough the Use of Parallel GPU Calculations: Initial Results LECTURE 5 Farid Monsefi (SWEDEN) Mälardalen University, School of Education, Culture and Communication (UKK) & School of Innovation, Design and Engineering (IDT) Title: Solution of Two-Dimensional Electromagnetic Scattering Problem by FDTD with Optimal Step Size, Based on a Semi-Norm Analysis 15:15 15:30 COFFEE BREAK LECTURE 6 Christian Sohl (SWEDEN) 15:30 16:15 16:20 17:00 Saab Electronic Defence Systems, Saab AB Title: Radar Cross Section Analysis in 2D Using an Integral Equation Method with Global Basis Functions LECTURE 7 Karl Lundengård (SWEDEN) Mälardalen University, School of Education, Culture and Communication (UKK) Title: An Examination of Some Fundamental Properties of the Multi-peaked Analytically Extended Function

3 Lecture 1: Maxwell Equations, Differential Forms, Yang-Mills Theory and Connections Victor Abramov Institute of Mathematics, University of Tartu Tartu, Estonia Abstract: The differentials forms with exterior differential is a powerful tool of a calculus of modern differential geometry. We explain the geometrical meaning of a differential form, describe the wedge product of differential forms and the exterior differential. We apply a calculus of differential forms to electromagnetic field theory and show that the Maxwell equations can be written in a beautiful and compact form by means of differential forms and exterior differential. We consider the Maxwell theory as an Abelian gauge theory with U(1) as the gauge group and show that potentials of electromagnetic field theory can be introduced with the help of localization of gauge parameter in order to restore the broken symmetry of Lagrangian as it was proposed by H. Weyl. Biography: Victor Abramov was born in Tallinn (Estonia) in He graduated the University of Tartu (Estonia) in 1981, and he received his PhD in mathematics at the Byelorussian State University in At present he is professor of geometry and topology at the Institute of Mathematics, University of Tartu. His research interests include the applications of methods of differential geometry to gauge field theories and topological field theories, supersymmetries and the theory of super manifolds, BRST-symmetries and applications of ternary algebraic structures in theoretical physics (quarks).

4 Lecture 2: The Evanescent Solutions of the Maxwell Equations Jean-Pierre Bérenger LEAT Université Nice Sophia Antipolis CNRS Nice, France Abstract: In this talk the new results on evanescent solutions of Maxwell equations will be presented.

5 Lecture 3: Application of the Green s Function to the Quasi-Stationary Analysis of Grounding Systems in Non-Homogeneous Soil Nenad Cvetković University of Niš, ELFAK Niš, Serbia Abstract: Different technological systems like power facilities, telecommunication systems, or lightning protection systems include a grounding system as a necessary part. Very often, the characterization of such grounding systems demands analysis of the influence of different kinds of ground inhomogeneities on grounding features. Such inhomogeneities can be roads, vertical containers having semi-spherical bases with a lower one buried in the ground, pillar ground electrodes with concrete foundation, or large holes in the ground (e.g. ponds and small lakes) filled with water. Corresponding procedures consider approximation of existing ground inhomogeneities with variously shaped homogeneous domains, including semi-cylindrically and semi-spherically-shaped ones, of known electromagnetic characteristics. In this lecture, procedures for analyzing influence of above-mentioned grounding inhomogeneities based on the usage of the quasi-stationary Green s function for spherically and cylindrically-shaped domains and image theory are presented. The talk will include explanation of the procedures for deriving the Green s functions, and some specific applications. Biography: Nenad N. Cvetković was born in Niš, Serbia in He received the Dipl. ing, M.Sc. and Ph.D. degrees from the Faculty of Electronic Engineering of University of Niš in 1995, 2002 and 2009, respectively. He is engaged as an assistant professor at the Department of Theoretical Electrical Engineering, Faculty of Electronic Engineering of Niš. His research interests are numerical methods for electromagnetic field calculation, especially in transmission line and grounding systems analysis. As an author or co-author, he has published about eighty papers in international journals or conference proceedings, one monograph dealing with grounding systems, and two textbooks. Cvetković is a reviewer for the COMPEL, IEEE Transactions on Electromagnetic Compatibility, and AEU (International Journal of Electronics and Communications) journals. He is a member of the Review board of the Safety Engineering Journal. He is a member of the IEEE Electromagnetic Compatibility Society, and the IEEE Magnetics Society.

6 Lecture 4: Reducing the Computational Time of Inverse Scattering Problems Thorough the Use of Parallel GPU Calculations: Initial Results Magnus Otterskog Mälardalen University, IDT Västerås, Sweden Abstract: Microwave tomography is a model based imaging technique that requires an accurate computer model of the measurement scenario. For complex objects like the human body a reasonable resolution of the resulting image results in a large computational problem in order to solve both the forward electromagnetic problem as well as the inverse problem. For 3D scenarios computational times of several hours or even days are reported in the literature and the need for speed up is obvious. The lecture presents initial results using a GPU for parallel computation of a scalable numerical electromagnetic problem. Comparison with sequential calculations on CPU:s are made and presented. The maximum obtained speed up factor is almost 70 between CPU and GPU use. Biography: Magnus Otterskog was born in Arboga, Sweden in He received the Master of Science and Tech.Dr. from Örebro University in 1999 and 2006 respectively. Since 2008 he works as a Senior Lecturer at Mälardalen University. His main research interests are electromagnetic wave propagation and radio frequency measurement techniques. For the moment he is running a project in biomedical engineering that aims towards a new imaging modality using microwaves for breast cancer detection.

7 Lecture 5: Solution of Two-Dimensional Electromagnetic Scattering Problem by FDTD with Optimal Step Size, Based on a Semi-Norm Analysis Farid Monsefi Mälardalen University, UKK and IDT Västerås, Sweden Abstract: To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD) method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell's curl equations, is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTD scheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source of electromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of Absorbing Boundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC) surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTD scheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of the computer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can be rather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTD algorithm. Biography: Farid Monsefi was born in Kermanshah, Iran, in He received the M.Sc. and licentiate degrees from Luleå University, Faculty of Applied Mathematics and Electronic Engineering, Sweden, in 2004, and As a Ph.D. candidate, Farid Monsefi started his doctoral studies in In these studies, he was doing research regarding the direct and inverse electromagnetic scattering problem applied to detection of human female breast cancer using microwave methods. He is nowadays the author or co-author of several papers, published and presented at different international conferences. His research interests include computational electromagnetics, mathematical modeling and scientific computing. Farid Monsefi was working as a consulting engineer during with different projects within electromagnetic compatibility, computational electromagnetics, and antenna analysis. The costumers were, among others, ABB FACTS and Bombardier in Västerås, Sweden. As a consulting engineer he participated in the highly advanced flatness control project, an ABB Force Measurements world-leading technology within cold processing of metals. In this project he used scientific computing and numerical analysis applied to the engineering control system of metals flatness.

8 Lecture 6: Radar Cross Section Analysis in 2D Using an Integral Equation Method with Global Basis Functions Christian Sohl Saab Electronic Defence Systems, Saab AB Stockholm, Sweden Abstract: The two-dimensional scattering problem of a perfectly conducting cylinder of arbitrary cross section is examined using an integral equation method with global basis functions. Both the Dirichlet and Neumann problems are considered, and explicit expressions are derived and compared to the classical Mie series expansion for the circular cylinder. Biography: Biography: Christian Sohl received the Ph.D. degree in Engineering in 2008, the Licentiate degree in Engineering in 2007, and the M.Sc. degree in Engineering Physics in 2000, all from Lund University, Lund, Sweden. As a Specialist in Antennas at Saab Electronic Defence Systems, Saab AB, Sweden, he is working with antenna and microwave engineering for radar, electronic warfare, and electronic surveillance. During the years he was a Postdoctoral Research Fellow in Electromagnetic Theory at Lund University, Lund, Sweden. His main research interests are in field and wave electromagnetics, especially scattering of electromagnetic waves and antenna theory.

9 Lecture 7: An examination of some fundamental properties of the multi-peaked analytically extended function Karl Lundengård Mälardalen University, UKK Västerås, Sweden Abstract: In this lecture a multi-peaked version of the analytically extended function (AEF) intended for approximation of multi-peaked lightning current waveforms will be presented along with some of its basic properties. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as a given charge transfer and specific energy will also be described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach will be discussed. Biography: Karl Lundengård was born in Everöd, Sweden, in After completing a M.Sc. in Engineering Physics from Lund University in 2011 he was accepted as a Ph.D. student at Mälardalen University in He currently works halftime as a lecturer at Mälardalen University and halftime as a Ph.D. student. His main area of research is the Vandermonde matrix and its applications as well as related matrices. Current projects include approximation of lightning current waveforms, lattice methods for pricing of financial derivatives and optimisation of the Vandermonde determinant and its generalizations on certain surfaces.